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pickupchik [31]

3 years ago

15

The cafe where you work just ran out of coffee, and you are at the store to buy 1 1/2pounds of coffee. You have put a can with 3

/4 pound of coffee into your shopping cart. How many more pounds of coffee do you need?

1 answer:

Semenov [28]3 years ago

7 0

Answer:

3/4

Step-by-step explanation:

3/4 + 3/4 = 1 1/2.

Easy.

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The face of the triangular concrete panel shown has an area of 22 square meters, and its base is 3 meters longer than twice its

Elodia [21]

Answer:

The length of the base is 11 meters.

Step-by-step explanation:

The diagram of the triangle is not shown; However, the given details are enough to solve this question.

Given

<em>Shape: Triangle</em>

<em>Represent the height with h and the base with b</em>

$b = 3 + 2h$

$Area = 22$

Required

Find the length of the base

The area of a triangle is calculated as thus;

$Area = \frac{1}{2} * b * h$

Substitute 22 for Area and 3 + 2h for b

The formula becomes

$22 = \frac{1}{2} * (3 + 2h) * h$

Multiply both sides by 2

$2 * 22 = 2 * \frac{1}{2} * (3 + 2h) * h$

$44 = (3 + 2h) * h$

Open the bracket

$44 = 3 * h + 2h * h$

$44 = 3h + 2h^2$

Subtract 44 from both sides

$44 - 44 = 3h + 2h^2 - 44$

$0 = 3h + 2h^2 - 44$

Rearrange

$0 = 2h^2 +3h - 44$

$2h^2 +3h - 44 = 0$

At this point, we have a quadratic equation; which is solved as follows:

$2h^2 +3h - 44 = 0$

$2h^2 + 11h - 8h - 44 = 0$

$h(2h + 11) - 4(2h + 11) = 0$

$(h - 4)(2h + 11) = 0$

Split the above

$(h - 4) = 0\ or\ (2h + 11) = 0$

$h - 4 = 0\ or\ 2h + 11 = 0$

Solve the above linear equations separately

$h - 4 = 0$

Add 4 to both sides

$h - 4 + 4 = 0 + 4$

$h = 0 + 4$

$h = 4$ ---- <em>First value of h</em>

$2h + 11 = 0$

Subtract 11 from both sides

$2h + 11 - 11 = 0 - 11$

$2h = 0 - 11$

$2h = -11$

Divide both sides by 2

$\frac{2h}{2} = -\frac{11}{2}$

$h = -\frac{11}{2}$ <em> ------ Second value of h</em>

Since height can be negative, we'll discard $h = -\frac{11}{2}$

Hence, the usable value of height is $h = 4$

Recall that $b = 3 + 2h$

Substitute 4 for h

$b = 3 + 2(4)$

$b = 3 + 8$

$b = 11$

Hence, the length of the base is 11 meters

3 0

3 years ago

PLEASE HELP ME ON THESE PROBLEMS, ITS URGENT! (Help for any of these would be greatly appreciated!)

Anvisha [2.4K]

1.) We can solve the problem by developing a linear model.
Let x represent the quantity to be used of the grade of coffee that sells for $70 per pound, and y represent the quantity to be used of the grade of coffee that sells for $80 per pound, then
$\left\begin{array}{c}x+y=80 . . . (1)\\70x+80y=76(80) . . . (2)\end{array}\right \\ \\ \Rightarrow \left\begin{array}{c}80x+80y=6400 . . . (3)\\70x+80y=6080 . . . (4)\end{array}\right \\ \\ \Rightarrow10x=320 \\ \\ \Rightarrow x=32 \\ \\ \Rightarrow y=80-32=48$
Therefore, 32 pounds of the grade of coffee that sells for $70 per pound, and 48 pounds of the grade of coffee that sells for $80 per pound should be used.

2.) Volume of alcohol in the original mixture
$\frac{35}{100} \times 40=14$ quarts

Let x be the number of quarts of alcohol to be added, then
Volume of alcohol in the new mixture
$\frac{48}{100} \times (40+x)=14+x \\ \\ \Rightarrow19.2+0.48x=14+x \\ \\ \Rightarrow0.52x=5.2 \\ \\ \Rightarrow x=10$

Therefore, 10 quarts of pure alcohol should be added

3.) Original proportion of white paint in the mixture
$=\frac{5}{5+11}=\frac{5}{16}$

Let x be the number of gallons of white paint to be added, then
$\frac{5+x}{16+x}=\frac{2}{3} \\ \\ \Rightarrow3(5+x)=2(16+x) \\ \\ \Rightarrow15+3x=32+2x \\ \\ \Rightarrow x=32-15=17$
Therefore, 17 gallons of white paint should be added.

4a.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 25 \\ \\ \Rightarrow3x=25\Rightarrow x=8.33$
which is not an integer.
Hence, the sum of three consecutive odd integers cannot be 25.

4b.) Let the three consecutive odd integers be x - 2, x and x + 2, then
$x - 2 + x + x + 2 = 45 \\ \\ \Rightarrow3x=45\Rightarrow x=15$
Thus, the three consecutive odd intergers whose sum is 45 are 13, 15 and 17.

5.) If all pipes are open and the tank was initially empty, let t be the time it will take to fill the tank, then
$\frac{1}{t} = \frac{1}{9} + \frac{1}{12} - \frac{1}{15} = \frac{20+15-12}{180} = \frac{23}{180} \\ \\ \Rightarrow t= \frac{180}{23} =7.83$
Therefore, it will take 7.83 hours to get the tank filled up.

3 0

3 years ago

The table shows the relationship between r and s, where s is the independent variable.

Viktor [21]

Answer:

Step-by-step explanation:

R=S -5/6

3 0

2 years ago

HELP PLEASE ONE QUESTION I DONT GET IT 6th GRADE MATH

grigory [225]

Answer:

-2.65

Step-by-step explanation:

-1.2 - 1.45 = -2.65

you could just simplify fraction into decimal and use calculator

8 0

3 years ago

Read 2 more answers

10 Points to the person who can help me. (What is the domain and range of the relation shown in the table?)

Firdavs [7]

Where is the table?.............?

4 0

3 years ago

Read 2 more answers